Question:
A test consists of 6 multiple choice questions, each having 4 alternative answers of which only one is correct. The number of ways, in which a candidate answers all six questions such that exactly four of the answers are correct, is __________.
A test consists of 6 multiple choice questions, each having 4 alternative answers of which only one is correct. The number of ways, in which a candidate answers all six questions such that exactly four of the answers are correct, is __________.
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Choose which 4 questions are answered correctly, then count the wrong choices for the remaining 2.
Updated On: Nov 5, 2026
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Correct Answer: 135
Solution and Explanation
Choose the 4 correctly answered questions: \(\binom{6}{4} = 15\) ways (each has exactly 1 correct choice).
Each of the remaining 2 questions must be answered wrongly: \(3\) wrong options each, so \(3 \times 3 = 9\) ways.
Total \(= 15 \times 9 = 135\).
Answer: 135
Each of the remaining 2 questions must be answered wrongly: \(3\) wrong options each, so \(3 \times 3 = 9\) ways.
Total \(= 15 \times 9 = 135\).
Answer: 135
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